Peter and Roman,
thanks for these hints... very useful. Obviously there is now also
a "BandedMatrix" Method option.
While it is obviously possible to find out the nitty critty (and
sometimes "mission-critical") details on how to use the Eigenvalues
function by some clever tricks, I still think that by now especially
a "classic" like Arnoldi should have been properly documented in
the official and current documentation. Just see how some more recently
developed really exotic functions in Mathematica are really extensively
documented with many details and options. (Alternatively for comparison
look into the documentation of eigensolvers of the competition of
Mathematica.)
Michael Weyrauch
Am 27.11.2010 09:48, schrieb Roman:
> On Nov 26, 11:30 am, Peter Pein<pet... at dordos.net> wrote:
>> Am Mon, 22 Nov 2010 12:35:46 +0000 (UTC)
>> schrieb Murray Eisenberg<mur... at math.umass.edu>:
>>
>>> This is definitely a gap in the documentation.
>>
>>> To find out that Eigenvalues has a Method option is easy, though:
>>
>>> Options[Eigenvalues]
>>> {Cubics -> False, Method -> Automatic, Quartics -> False}
>>
>>> What is difficult (impossible), however, is to find out for a Method
>>> option -- and a number of functions have it -- is what the possible
>>> settings are.
>>
>> ...
>>
>> Eigenvalues[HilbertMatrix[4],Method->"foo"]
>> Eigenvalues::emeth: The method specified by Method -> foo should be
>> either Automatic, Arnoldi, or BandedMatrix.
>>
>> works often, not always.
>
> Michael,
> This is the method I used in the past, plus some info from the ARPACK
> documentation (since this is what the Arnoldi method ends up calling
> internally). I've summarized the resulting documentation here:
>
> http://groups.google.com/group/comp.soft-sys.math.mathematica/browse_thread/thread/2a41064c0dbe5d54/26f379d722f6e1c8?hl=en#26f379d722f6e1c8
> Roman
>